# Combined effects of local and nonlocal hybridization on formation and condensation of excitons in the extended Falicov-Kimball model

## TL;DR

This study investigates how local and nonlocal hybridization influence exciton formation and condensation in the extended Falicov-Kimball model, revealing their roles in different momentum condensates and explaining experimental resistivity anomalies.

## Contribution

It demonstrates the distinct effects of local and nonlocal hybridization on excitonic states and their combined impact within the extended Falicov-Kimball model using DMRG methods.

## Key findings

- Local hybridization supports q=0 condensate formation.
- Nonlocal hybridization supports q=π condensate formation.
- Hybridization enhances excitonic correlations and affects ground-state properties.

## Abstract

We study the combined effects of local and nonlocal hybridization on the formation and condensation of the excitonic bound states in the extended Falicov-Kimball model by the density-matrix-renormalization-group (DMRG) method. Analysing the resultant behaviours of the excitonic momentum distribution $N(q)$ we found, that unlike the local hybridization $V$, which supports the formation of the $q=0$ momentum condensate, the nonlocal hybridization $V_n$ supports the formation of the $q=\pi$ momentum condensate. The combined effect of local and nonlocal hybridization further enhances the excitonic correlations in $q=0$ as well as $q=\pi$ state, especially for $V$ and $V_n$ values from the charge-density-wave (CDW) region. Strong effects of local and nonlocal hybridization are observed also for other ground-state quantities of the model such as the $f$-electron density, or the density of unbound $d$-electrons, which are generally enhanced with increasing $V$ and $V_n$. The same calculations performed for nonzero values of $f$-level energy $E_f$ revealed that this model can yield a reasonable explanation for the pressure-induced resistivity anomaly observed experimentally in $TmSe_{0.45}Te_{0.55}$ compound.